A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod?

Question

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

3.7 rad/s2

1.3 rad/s2

2.5 rad/s2

4.9 rad/s2

1.9 rad/s2

Answer 1

Let:

m be the mass,

a be the angular acceleration.

Taking moments about the pivot:

m * 9.81 * 2.0 cos(70) / 2 = ma * 2.0^2 / 3

a = 2.5 rad / s^2.